Global optimization applied to the oscillator problem

The oscillator problem consists of determining good initial values for the node voltages and the frequency of oscillation and the avoidance of the DC solution. Standard approaches for limit cycle calculations of autonomous circuitry exhibit poor convergence behavior in practice. By introducing an additional periodic probe voltage source to the oscillator circuit, the system of autonomous differential algebraic equations (DAEs) can be reformulated as a system of non-autonomous DAEs with the constraint, that the current through the source has to be zero for the limit cycle. Using a two stage approach leads to a greater range of convergence as the standard approach, but the success of the algorithm is heavily dependent on the initial amplitude of the probe source and the frequency of oscillation. This paper presents a fast and reliable optimization based initialization procedure which overcomes the initialization problem of the two stage algorithm